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Unformatted text preview: Fluids Lecture 1 Notes 1. Formation of Lifting Flow Reading: Anderson 4.5 4.6 Formation of Lifting Flow Conservation of Circulation Kelvins Theorem The circulation about any closed circuit is defined to be vector V dvectors = vector n dA where dvectors is an arc length element of the circuit, and vector V is the local ow velocity. The equivalent vorticity area integral form follows from Stokes Theorem. In 2-D, this second form is = dA (In 2-D) To investigate the formation of a lifting ow about an airfoil, we now consider the circulation about a circuit demarked by uid elements which are drifting with the ow (a fine smoke ring would constitute such a circuit). Because both the shape of the circuit and the velocities V ds dA seen by the circuit will in general change in time, there is the possibility that ( t ) will change in time as well. The rate of change of this circulation is d d D = dA = ( dA )...
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